Tallennettuna:
| Päätekijät: | , , , |
|---|---|
| Aineistotyyppi: | Preprint |
| Julkaistu: |
2024
|
| Aiheet: | |
| Linkit: | https://arxiv.org/abs/2402.09024 |
| Tagit: |
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Sisällysluettelo:
- The $λ$$Π$-calculus modulo theory is an extension of simply typed $λ$-calculus with dependent types and user-defined rewrite rules. We show that it is possible to replace the rewrite rules of a theory of the $λ$$Π$-calculus modulo theory by equational axioms, when this theory features the notions of proposition and proof, while maintaining the same expressiveness. To do so, we introduce in the target theory a heterogeneous equality, and we build a translation that replaces each use of the conversion rule by the insertion of a transport. At the end, the theory with rewrite rules is a conservative extension of the theory with axioms.